Publications of Serge Richard


  a) Refereed Full Papers
 
  39) Quantum walks with an anisotropic coin I: spectral theory,
with A. Suzuki and R. Tiedra de Aldecoa, submitted.
 
  38) Does Levinson's theorem count complex eigenvalues ?
with F. Nicoleau and D. Parra, submitted.
 
  37) Spectral and scattering theory for Schroedinger operators on perturbed topological crystals,
with D. Parra, submitted.
 
  36) On Schroedinger operators with inverse square potentials on the half-line,
with J. Derezinski, Ann. Henri Poincaré 18 (2017), 869 – 928.
 
  35) Commutator criteria for strong mixing II. More general and simpler,
with R. Tiedra de Aldecoa, submitted.
 
  34) Continuity of the spectra for families of magnetic operators on Z^d,
with D. Parra, Anal. Math. Phys. 6 (2016), 327 - 343.
 
  33) Schroedinger operators with n positive eigenvalues: an explicit construction involving complex valued potentials,
with J. Uchiyama and T. Umeda, Proc. Japan Acad. 92, Ser. A (2016), 7 - 12.
 
  32) Spectral and scattering properties at thresholds for the Laplacian in a half-space with a periodic boundary condition,
with R. Tiedra de Aldecoa, J. Math. Anal. Appl. 446 (2017), 1695 - 1722.
 
  31) One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results,
with K. Pankrashkin, J. Math. Phys. 55 (2014), 062305-1 - 062305-17.
 
  30) Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides,
with R. Tiedra de Aldecoa, Bull. Soc. math. France 144 (2016), 251 - 277.
 
  29) Explicit formulas for the Schroedinger wave operators in R^2 ,
with R. Tiedra de Aldecoa, C. R. Acad. Sci. Paris, Ser. I. 351 (2013), 209 - 214.
 
  28) New expressions for the wave operators of Schroedinger operators in R^3,
with R. Tiedra de Aldecoa, Lett. Math. Phys. 103 (2013), 1207 - 1221.
 
  27) Low energy spectral and scattering theory for relativistic Schroedinger operators,
with T. Umeda, Hokkaido Mathematical Journal 45 (2016), 141 - 179.
 
  26) Commutator methods for unitary operators,
with C. Fernandez and R. Tiedra de Aldecoa, J. Spectr. Theory 3 (2013), 271 – 292.
 
  25) On the wave operators for the Friedrichs-Faddeev model,
with H. Isozaki, Ann. Henri Poincaré 13 (2012), 1469 – 1482.
 
  24) Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends,
with R. Tiedra de Aldecoa, Rev. Math. Phys. 25 (2013), 1350003-1 - 1350003-40.
 
  23) A few results on Mourre theory in a two-Hilbert spaces setting,
with R. Tiedra de Aldecoa, Anal. Math. Phys. 3 (2013), 183 - 200.
 
  22) Levinson's theorem and higher degree traces for Aharonov-Bohm operators,
with J. Kellendonk and K. Pankrashkin, J. Math. Phys. 52 (2011), 052102-1 - 052102-28.
 
  21) On the wave operators and Levinson's theorem for potential scattering in R^3,
with J. Kellendonk, Asian-European Journal of Mathematics 5 (2012) 1250004-1 - 1250004-22.
 
  20) Positive quantization in the presence of a variable magnetic field,
with M. Mantoiu and R. Purice, J. Math. Phys. 52 (2011), 112101-1 - 112101-15.
 
  19) Time delay is a common feature of quantum scattering theory,
with R. Tiedra de Aldecoa, J. Math. Anal. Appl. 387 (2012), 618 – 630.
 
  18) Spectral and scattering theory for the Aharonov-Bohm operators,
with K. Pankrashkin, Rev. Math. Phys. 23 (2011), 53 - 81.
 
  17) Coherent states in the presence of a variable magnetic field,
with M. Mantoiu and R. Purice, International Journal of Geometric Methods in Modern Physics 8 (2011), 187 - 202.
 
  16) Magnetic pseudodifferential operators with coefficients in C*-algebras,
with M. Lein and M. Mantoiu, Publ. RIMS, Kyoto Univ. 46 (2010), 755 - 788.
 
  15) New formulae for the wave operators for a rank one interaction,
with R. Tiedra de Aldecoa, Integral Equations and Operator Theory 66 (2010), 283 - 292.
 
  14) The method of the weakly conjugate operator: Extensions and applications to operators on graphs and groups,
with M. Mantoiu and R. Tiedra de Aldecoa, Petroleum - Gas University of Ploiesti Bulletin, Mathematics - informatics - physics Series LXI (2009), 1 - 12.
 
  13) Weber-Schafheitlin type integrals with exponent 1,
with J. Kellendonk, Integral Transforms and Special Functions 20 (2009), 147 - 153.
 
  12) On the structure of the wave operators in one dimensional potential scattering,
with J. Kellendonk, Mathematical Physics Electronic Journal 14 (2008), 1 - 21.
 
  11) The topological meaning of Levinson's theorem, half-bound states included,
with J. Kellendonk, J. Phys. A: Math. Theor. 41 (2008), 295207.
 
  10) On the spectrum of magnetic Dirac operators with Coulomb-type perturbations,
with R. Tiedra de Aldecoa, J. Funct. Ana. 250 (2007), 625 - 641.
 
  9) Spectral analysis for adjacency operators on graphs,
with M. Mantoiu and R. Tiedra de Aldecoa, Ann. Henri Poincaré 8 (2007), 1401 - 1423.
 
  8) Spectral and propagation results for magnetic Schrödinger operators; a C*-algebraic framework,
with M. Mantoiu and R. Purice, J. Funct. Ana. 250 (2007), 42 - 67.
 
  7) On the essential spectrum of magnetic pseudodifferential operators,
with M. Mantoiu and R. Purice, C. R. Acad. Sci. Paris, Ser. I 344 (2007), 11 - 14.
 
  6) Levinson's theorem for Schrödinger operators with point interaction: a topological approach,
with J. Kellendonk, J. Phys. A: Math Gen. 39 (2006), 14397 - 14403.
 
  5) Some improvements in the method of the weakly conjugate operator,
Letters in Mathematical Physics 76 (2006), 27 - 36.
 
  4) Spectral and scattering theory for Schrödinger operators with Cartesian anisotropy,
Publ. RIMS, Kyoto Univ. 41 (2005), 73 - 111.
 
  3) On perturbations of Dirac operators with variable magnetic field of constant direction,
with R. Tiedra de Aldecoa, J. Math. Phys. 45 (2004), 4164 - 4173.
 
  2) Minimal escape velocities for unitary evolution groups,
Ann. Henri Poincaré 5 (2004), 915 - 928.
 
  1) Absence of singular spectrum for Schrödinger operators with anisotropic potentials and magnetic fields,
with M. Mantoiu, J. Math. Phys. 41 (2000), 2732 - 2740.
 
  b) Refereed Conference Publications
 
  b5) Levinson's theorem: an index theorem in scattering theory,
in Proceedings of the Conference Spectral Theory and Mathematical Physics, Santiago 2014, Operator Theory Advances and Applications 254, 149 – 203, Birkhäuser, 2016.
 
  b4) A new formula relating localisation operators to time operators,
with R. Tiedra de Aldecoa, in Spectral Analysis of Quantum Hamiltonians, Operator Theory: Advances and Applications 224, 301 – 338, Birkhäuser/Springer, Basel, 2012.
 
  b3) New formulae for the Aharonov-Bohm wave operators,
Spectral and Scattering Theory for Quantum Magnetic Systems, 159 - 168, Contemporary Mathematics 500, AMS, Providence, Rhode Island, 2009.
 
  b2) Topological boundary maps in physics: General theory and applications,
with J. Kellendonk, Perspectives in Operator Algebras and Mathematical Physics, 105 - 121, Theta, Bucharest, 2008.
 
  b1) Twisted crossed products and magnetic pseudodifferential operators,
with M. Mantoiu and R. Purice, Advances in Operator Algebras and Mathematical Physics, 137 - 172, Theta Ser. Adv. Math. 5, Theta, Bucharest, 2005.
 
  c) Non-refereed Conference Publications
 
  c2) Inner and outer continuity of the spectra for families of magnetic operators on Z^d ,
RIMS Kokyuroku 2023, 69 - 76, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 2017.
 
  c1) Time delay for an abstract quantum scattering process,
RIMS Kokyuroku 1760, 33 - 43, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 2011.
 
  d) Theses
 
  d3) A few results in scattering theory: Time operator, time delay, Mourre theory and topological Levinson's theorems,
HDR Thesis (2011), University of Lyon.
 
  d2) Commutator methods in spectral and scattering theory,
(partially in French), PhD Thesis (2004), University of Geneva.
 
  d1) Analyse spectrale d'hamiltoniens à champ magnétique pour des systèmes bidimensionnels,
(French), Diploma Thesis (1999), University of Lausanne.